WHY EVEN WASTE OUR TIME SHOWING US ONLY PART OF THE CIRCUIT?????
And why would anybody suggest replacing an unknown device with a random assembly???
AND, why even purchase a replacement timer that did not provide the required delay???
ALL honest manufacturers will state the time delay of a timer that they sell, any that do not are immediately suspect, as I see it.

 

i am more concerned that elevator techs are not sure how to wire a simple device like timer...

based on posts #6, #9 and #11, this has to be Timer ON. it is powered by DC that is rectified but not filtered which was common half a century ago but this could be a problem for modern devices (retriggering, voltage peaks...).

getting exact replacement is likely difficult. getting existing design reverse engineered and repaired or replicated should be very straight forward if sample is available or at least good pictures (with clear cover removed).

functionally it seem to be one of the following two arrangements (here shown with switching on positive side):


if replacing by some contemporary product, two options exist:
modify panel wiring to match the replacement device, or...
leave existing panel wiring as is, make a wiring adapter or "extension cable" that allows replacement to plug into existing panel

the second option offers some advantages such as no altering of existing wiring panel wiring, the only custom part is the socket adapter or harness, it is easy to plug in and try... and remove if you get hold of original parts (repaired or cloned).

for example something like this may work:
https://www.ia.omron.com/product/item/3769/

which does have different pinout...

 

Consider that the device assembly we se in post #1, that should be quite simple to repair, IF we had been given the whole circuit instead of just a small portion. Or is that all that the TS had?? I am asking about the circuit INSIDE the plug in module, not what is surrounding it.
IF the TS can undo the four screws and slide the PCB out of the plastic case, then we can have a clear view of the whole assembly and probably provide whatever solution is required.
ALSO, based on what I see, NONE!! of the commercial time delay relays will have the same pin-out as what is present. THAT means a major wiring change, and the two elevator service folks that I have met will not know any more than my friend's cat about how to rewire for the replacement timer.
(The cat is quite smart, but has not had any technical training.)

 

In post#11 we see in the one picture another timer plugged into the socket next to the empty one. Is that the timer that has too short a delay??
And is the complaint that the delay is suddenly not long enough?? Or that the requirements have changed, or something else?? Most plug in timers have an adjustable time delay. I AM AWARE that many companies choose to use non-standard pinouts so that only they can provide service parts.

 

Find someone who can reverse engineer the board and its function. Then make new boards from a new design.

The first step would be to take a unit apart and post sharp photos of both sides of the board.
Make notes of the pin connections.

You will find that in this forum there are quite a few who can reverse engineer the present module.

 

and have fun doing it...

 

Guess all you want to here the OP needs to open it up and give good pictures

 

IF the circuit in the container is actually a timer, that is what it will take. But there is information not presented. Such asjust exactly is the complaint. Or serious problem to be solved.